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Answer & Step-by-step explanation:

To get the range of the function y = 2x + 1, we need to determine the set of all possible output values (y) that the function can produce for the given domain.

When x = -2, y = 2(-2) + 1 = -3.

When x = 4, y = 2(4) + 1 = 9.

When x = 6, y = 2(6) + 1 = 13.

So, the output values (y) for the given domain { -2, 4, 6 } are -3, 9, and 13.

Line 1 and line 3 are parallel and line 1 and line 2 are perpendicular.

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

y = -5/2 x -1

4x-10y = 8

2y = -5x+7

line 1, m = -5/2

line 2, m = 2/5

line 3, m -5/2

Hence, Line 1 and line 3 are parallel and line 1 and line 2 are perpendicular.

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Answer: 22v-4

Step-by-step explanation: four less than means subtract and product means multiply

Answer:

y=40x+35

Step-by-step explanation:

After 0 months, she still needs to pay the first $35. This means that this is her y-intercept, and in the formula “y=mx+b”, it would go in the “b” place. Then x would mean how many months have passed, so therefore 40 would go into the “m” place. If you put that together, it looks like “y=40x+35”.

The simplification of the given polynomial is az-bz+3b²-6ab+3a².

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given polynomial (a-b)·z+3(b-a)².

Here, (a-b)·z+3(b²-2ab+a²)

= z·(a-b)+3b²-6ab+3a²

= az-bz+3b²-6ab+3a²

Therefore, the simplification of the given polynomial is az-bz+3b²-6ab+3a².

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The equation which can be used to represent the situation is 396 = x - 0.2x

The original price of the love seat was $495.

Let

Original price of the love seat= x

New price= $396

Percentage discount= 20%

396 = x - (20% of x)

396 = x - 0.2x

396 = 0.8x

divide both sides by 0.8

x = 396 / 0.8

x = $495

Hence, the equation 396 = x - 0.2x is used to solve the question and the original price is $596

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The measure of each Angle is 80, 50 and 50 degree.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

<H= 4x- 20

and, <G = 2x

and, <I = 2x

Now, In triangle GHI using Angle Sum Property

<G+ <H+ <I= 180

4x- 20 + 2x+ 2x = 180

8x - 20 = 180

8x = 200

x= 25

So, the measure of <G = 4x- 20 = 100 -20 = 80 degree.

and, <H = <I= 2x= 2(25)= 50 degree

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The contrapositive statement is,

''If the corresponding angles of two triangles are not congruent, then the triangles are not congruent."

When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

Given:

A statement:

If two triangles are congruent, then their corresponding angles are congruent.

The contrapositive statement is,

''If the corresponding angles of two triangles are not congruent, then the triangles are not congruent."

Therefore, the D statement is correct.

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Answer:

12 lb of seed.

Step-by-step explanation:

We need to determine the amount of seed required for a 4800 sq ft lawn.

First, we need to find out how many 1200 sq ft portions the 4800 sq ft lawn is:

4800 sq ft / 1200 sq ft/portion = 4 portions

Next, we can use the seed manufacturer's recommendation of 3 lb of seed per 1200 sq ft:

3 lb/portion * 4 portions = 12 lb

Therefore, the architect will need 12 lb of seed.

Answer: The expression inside the parentheses can be simplified as follows:

24/16 + 3/3 = 3

So, the expression becomes:

6/11 - 3/12 = 6/11 - 1/4

Now we can subtract the two fractions:

6/11 - 1/4 = 6/11 - 4/11 = 2/11

So the final answer is 2/11.

Step-by-step explanation:

Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.

A deposit ticket is a little paper where you are required to fill in the details of the deposit that you seek to make into your savings account. All information in the ticket ought to be filled accurately.

here, we have,

The teller may have declined to receive the ticket due to incorrect total amount filled on the ticket. Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.

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A directed graph can be used to determine whether a relation R on a finite set A is asymmetric or not by checking whether there is any pair of elements (a, b) in R such that both (a, b) and (b, a) are present in R.

If such a pair exists, then the relation is not asymmetric because it violates the condition for asymmetry, which states that for any (a, b) in R, (b, a) cannot be in R.

In the directed graph, this means that there is a directed edge from a to b and also a directed edge from b to a. This would result in a cycle in the directed graph, which is not allowed in an asymmetric relation.

If there are no such pairs in R, then the relation is asymmetric, and the directed graph will not contain any cycles. Therefore, the directed graph can be a helpful tool to quickly determine if a relation is asymmetric or not, especially for larger sets A.

Since BD is a diameter of circle A, the slope of BD is equal to -2/3.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

By critically observing the geometric shape, we can reasonably infer and logically deduce that line segment BD is perpendicular to line segment BE.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

3/2 × m₂ = -1

3m₂ = -2

Slope, m₂ = -2/3.

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Complete Question:

In the diagram, BD is a diameter of circle A. If the slope of BE is 3/2, what is the slope of BD?

Step-by-step explanation:

distinct ways !

STATICS and STATICS are 2 different ways to arrange them. have you noticed the difference ?

no, of course not. I only exchanged the 2 S. the same problem with the 2 T.

while they are different permutations, their arrangements are not distinctly different. to us observers they look the same.

so, for the 7 letters, 7! is not the full answer.

these 7! permutations include all the ones, where we only change the S and the T with each other.

we need to eliminate those. we do this by dividing by the S permutations (2! = 2) and the T permutations (again, 2! = 2).

so, the answer is

7! / (2×2) = 5040 / 4 = 1260

the 7 letters can be arranged in 1260 distinctly different ways.

y' = (y-3)(y+3)exp(y)

This differential equation has equilibrium solutions at y=0 and y=3, and y' is positive for -inf < y < 0 and 3 < y < inf and negative for 0 < y < 3.

1. Set y′ = 0 to get the equilibrium solutions

y′ = 0 → y = 0 and y = 3

2. Find the sign of y′

y′ = (y-3)(y+3)exp(y)

For y < 0, y′ is positive

For 0 < y < 3, y′ is negative

For y > 3, y′ is positive

This differential equation has two equilibrium solutions at y=0 and y=3, meaning the value of y does not change when the equation is applied.

To determine the sign of the equation, we can look at the equation y′ = (y-3)(y+3)exp(y). For y < 0, y′ is positive. This means that when y is less than 0, the equation increases in value. For 0 < y < 3, y′ is negative. This means that when y is in between 0 and 3, the equation decreases in value. And for y > 3, y′ is positive. This means that when y is more than 3, the equation increases in value.

Overall, the equation behaves as expected: it increases when y is less than 0 and more than 3, and decreases when y is between 0 and 3. This is what we would expect in order for the equation to have the equilibrium solutions at y=0 and y=3.

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Answer: x = 8, x = -2

Step-by-step explanation:

(x - 3)² = 25

Step 1: Take the square root on each side of the equation.

(x - 3)² = 25

√(x - 3)² = ±√25

Step 2: After taking the square root on each side of the equation, this allows you to solve for x.

x - 3 = ±5

Solution 1

x - 3 = 5

x = 5 + 3

x = 8

Solution 2

x - 3 = - 5

x = -5 + 3

x = -2

Another way to solve this problem is to multiply (x - 3)² using the FOIL methods (first, outer, inner, last) and then set it equal to 25.

(x - 3) (x - 3) = 25

x² - 3x - 3x + 9 = 25

The next step is to add like terms. After adding like terms, solve for x.

x² - 3x - 3x + 9 = 25

x² - 6x + 9 - 25 = 25 - 25

x² - 6x - 16 = 0

Last step is to factor x² - 6x - 16 = 0 so you can solve for the two solutions.

(x - 8) (x + 2) = 0

Solution 1

x - 8 = 0

x = 8

Solution 2

x + 2 = 0

x = -2

Answer: 0.0208333333

Step-by-step explanation: one way you could do it is -->1/4 ≈ 0.25 and 1/12 ≈ 0.0833333333333333

so then

0.25 ÷ 0.0833333333333333 = 0.0208333333

If you'd like to check the answer, use a calculator.

1/4 ÷ 1/12 = 0.0208333333

hope this helps :)

Correct Answer: c. ordinal scale

What is the ordinal scale?

An ordinal scale is a type of measurement scale in which the data can be ranked or ordered based on the size or value of the measurement. The categories in an ordinal scale, such as "excellent," "very good," "good," and "poor," do not have equal intervals or a true zero point, so they cannot be used to perform mathematical operations. The main purpose of an ordinal scale is to order or rank the data based on relative position.

In this case, the restaurant's rating scale is an example of an ordinal scale because the customers are asked to indicate the quality of service on a scale with four categories, and the categories can be ranked in order from best to worst.

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The completed entries is added as an attachment

From the question, we have the following parameters that can be used in our computation:

3,723 ÷ 51

Express 3,723 as 2295 + 1428

So, we have the following representation

3,723 ÷ 51 = (2295 + 1428) ÷ 51

Expand the expression

So, we have the following representation

3,723 ÷ 51 = 2295 ÷ 51 + 1428 ÷ 51

Evaluate the quotients

3,723 ÷ 51 = 45 + 28

Next, we complete the blanks (see attachment) for the completed entries

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Answer:

1/4 cup and 4 tablespoons

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>

Let c= + < (  cos α,cos β ,cos γ )>

be the unit vectors (in opposite directions) orthogonal to a and b

the scalar product :

c.a =  cos α +cos β = 0

c.b =  cos α + cos γ = 0

It follows that ,

c= ± (  -cos α,cos α ,cos α )

cos α = ±1/√3

c= ± (-1/√3, 1/√3,1/√3 )

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

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The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

a=i+j = < 1,1,0 > , b=i+k = < 1,0,1>

Let c= + < (  cos α,cos β ,cos γ )>

be the unit vectors (in opposite directions) orthogonal to a and b

the scalar product :

c.a =  cos α +cos β = 0

c.b =  cos α + cos γ = 0

It follows that ,

c= ± (  -cos α,cos α ,cos α )

cos α = ±1/√3

c= ± (-1/√3, 1/√3,1/√3 )

The unit vectors that are orthogonal to both i+j and i+k are

± (-1/√3, 1/√3,1/√3 )

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The domains of the composite function (f/g)(4) and (f + g)(4) for f(x) = x² + 2x - 3 and g(x) = x² - 9 are equal to 3 and 28 respectively.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domains of the function (f/g)(4) and (f + g)(4) as follows:

(f/g) = (x² + 2x - 3)/(x² - 9)

by factorization of the right hand side;

(f/g) = (x - 1)(x + 3)/(x - 3)(x + 3)

(f/g) = (x - 1)/(x - 3)

(f/g)(4) = (4 - 1)/(4 - 3)

(f/g)(4) = 3

(f + g) = x² + 2x - 3 + x² - 9

(f + g) = 2x² + 2x - 12 {simplify like terms}

(f + g)(4) = 2(4)² + 2(4) - 12

(f + g)(4) = 28

Therefore, the domains of the composite function (f/g)(4) and (f + g)(4) for f(x) = x² + 2x - 3 and g(x) = x² - 9 are equal to 3 and 28 respectively.

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Answer: First one is -11

Second one is 0

Step-by-step explanation:

[ 61 ]

to solve this you need to use pythagorean theorem, and find the lengths of the sidesnof the triangle using two points.

x axis: 2 - ( -3 ) = 2 + 3 = 5

y axis: 2 - ( -4 ) = 2 + 4 = 6

PyTh: a^2 + b^2 = c^2

5^2 + 6^2 = c^2

25 + 36 = c^2

c = SqRt ( 61 )

Answer: C

Step-by-step explanation:

Again, let's use elimination.

Does it suggest a different interpretation than the rest of the article? Yes, because it indicates there is a flaw in saying that the data shows human and chimp similarities.

Is it a reason for pursuing DNA Research? Nope.

Does it specifiy the extent of similarity? Yup.

SO now we are down to A and C as possible choices.

C is the answer, because while the data can be used to produce a different interpretation, its purpose in developing the main idea is purely specification.

The correct statement comparing the values of the 8s in 2,7812 and 94894 is that the 8 in 2,7812 has a greater value than the 8 in 94894.

This is because the value of a digit in a number is determined by its place value. In the number 2,7812, the 8 is in the hundreds place, meaning it has a value of 800. In the number 94894, the 8 is in the tens place, meaning it has a value of 80.

Therefore, the 8 in 2,7812 has a greater value (800) than the 8 in 94894 (80).

Here is the answer in HTML format:

The correct statement comparing the values of the 8s in 2,7812 and 94894 is that the 8 in 2,7812 has a greater value than the 8 in 94894.

This is because the value of a digit in a number is determined by its place value. In the number 2,7812, the 8 is in the hundreds place, meaning it has a value of 800. In the number 94894, the 8 is in the tens place, meaning it has a value of 80.

Therefore, the 8 in 2,7812 has a greater value (800) than the 8 in 94894 (80).

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We have shown that for any eigenvalue λ of A, 1-λ is an eigenvalue of -A. So, the eigenvalues of -A are 1-λ1, 1-λ2, ..., 1-λn, where λ1, λ2, ..., λn are the eigenvalues of A.

Eigenvalues are scalar values that are associated with a linear transformation of a matrix and are used to represent the behavior of a linear system. They represent the factor by which a linear transformation scales the direction of a vector. Eigenvalues play an important role in many areas of mathematics, including linear algebra, physics, engineering, and statistics. If a matrix A has an eigenvector x and an eigenvalue λ, then A can be represented as a scalar multiplication of x by λ: A x = λ x. The eigenvalues of a matrix can be used to determine its stability, to find the diagonalization of the matrix, and to determine the eigenvectors that represent the most important directions of a linear transformation.

The eigenvalues of a matrix A are scalars that satisfy the equation Av = λv, where v is a non-zero eigenvector and λ is the corresponding eigenvalue. If λ is an eigenvalue of A, then 1-λ is an eigenvalue of -A.

To see why this is true, let's consider an eigenvector v of A with eigenvalue λ. Then, Av = λv. We can multiply both sides of this equation by -1 to obtain:

-Av = -λv

Now, we can substitute -A for A and 1-λ for λ:

(-A)v = (1-λ)v

Thus, we have shown that for any eigenvalue λ of A, 1-λ is an eigenvalue of -A. So, the eigenvalues of -A are 1-λ1, 1-λ2, ..., 1-λn, where λ1, λ2, ..., λn are the eigenvalues of A.

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Answer: The transformation matrix R for a rotation of 120° about an axis from the origin through the point (1,1,1) can be calculated using the formula:

R = I + (sin(θ))U + (1-cos(θ))UU'

where θ is the angle of rotation (120° in this case), I is the identity matrix, U is a skew-symmetric matrix, and U' is its transpose. The skew-symmetric matrix can be calculated as follows:

U = [0, -z, y; z, 0, -x; -y, x, 0]

where x, y, and z are the components of the vector (1,1,1) that defines the axis of rotation.

Plugging in the values and simplifying, the transformation matrix R is:

R = [ cos(120°), -sin(120°), 0; sin(120°), cos(120°), 0; 0, 0, 1 ]

Note: cos(120°) = -1/2 and sin(120°) = √(3)/2.

Step-by-step explanation:

Answer:

not possible

Step-by-step explanation:

it's not equal to zero, and the answer ends up with imaginary number